Simulation Study of Estimators of the Gamma Rate Parameter Using MLE as a Baseline Estimator

Classical estimation methods of the rate parameter of the gamma distribution have shown to have quality issues. In this paper we propose three estimators namely linear shrinkage, preliminary test and linear shrinkage preliminary test for rate parameter of the gamma distribution using maximum likelihood estimation as a baseline estimator. The salient feature of the proposed estimators is the optimality and robustness property that is defined on belief of an uncertain prior information (UPI). Expressions for bias and relative efficiency using Maximum Likelihood Estimation (MLE) as a baseline estimator have been derived with asymptotic properties. A Monte Carlo simulation work is carried out with degree of belief in the UPI. The study results shows that even though the proposed estimators utilizes the UPI from the neighbourhood of the true rate parameter, they are more efficient and minimally biased when prior information is closed to the neighbourhood of the rate parameter compared to the classical Maximum Likelihood Method.